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2 years ago

Rationalize the denominator 1/√3−1

Mathematics

2 answers:

Effectus [21]2 years ago

8 0

<h3><u>Solution</u><u>:</u></h3>

<u> $\frac{1}{ \sqrt{3} - 1 } \\ = \frac{1}{ \sqrt{3} - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{ \sqrt{3} + 1}{( \sqrt{3})^{2} - (1)^{2} } \\ = \frac{ \sqrt{3} + 1 }{3 - 1} \\ = \frac{ \sqrt{3} + 1}{2}$ </u>

<h3><u>Answer</u><u>:</u></h3>

dem82 [27]2 years ago

6 0

Multiply the fraction by the (denominator/denominator)
Which is equals to 1.

1/root3-1 * (1/root3-1) / (1/root3-1)

Now you have root3-1 / 2

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A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side

kari74 [83]

shortest side: 851

middle side:927

longest side : 1306

Explanation

Step 1

Let

x represents the shortest side

y represents the middle side

z represents the longest side

so, set the equations

a) the perimeter of a rectangle is the sum of the sides, so

$\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}$

b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)

$x=y-76\Rightarrow equation(2)$

c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)

$z=y+379\Rightarrow equation(3)$

Step 2

solve the equations

a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}$

now, replace the y value in equatino (2) to find x

$\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}$

c) finally, prelace x and y value in equation (1) to find z

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}$

shortest side: 851

middle side:927

longest side : 1306

I hope this helps you

4 0

7 months ago

A rectangular bin with an open top and volume of 38.72 cubic feet is to be built. The length of its base must be twice the width

KengaRu [80]

Answer:

Width=2.2 FT

Length=4.4 FT

Heigh= 4 FT

Step-by-step explanation:

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2 years ago

A cheetah ran 275 feet in 3.23 seconds. How fast did the cheetah run in miles per hour? Round your answer to the nearest whole m

yawa3891 [41]

First we convert feet into meters, since 1 feet is 0.3048 m: 275 feet * 0.3048 = 83.82m.

Then we do: 83.82m / 3.23s = <span>25.9504644 m/s.

Then we convert that into miles per hour by </span>2.23694, so we do:

25.9504644 * 2.23694 = <span>58.0496318.

Then we round it to 58 mph.

So the answer is: The cheetah was running at 58 mph.

Hope this helped! c:</span>

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2 years ago

40 green cars 20 silver if same # of green stayed the same how many more silver would need to be added so the ratio of green to

slega [8]

So, there will be 40 green cars. if we want the ratio to be 1:3, we will need there to b three times as many silver cars as green cars: 40*3=120.

we already have 20 silver, so we need to add 120-20, that is 100 silver cars!

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2 years ago

The formula for electrical power is P, is P= I^2 R, where I is current and R is resistance. The formula for I in terms of. P and

Butoxors [25]

Ans

I = sqrt(P/R)

Step-by-step explanation:

You divide both sides by R first

P/R = I^2 R/R

So,

I^2 = P/R

take the square root of both sides

I = sqrt(P/R)

7 0

2 years ago

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